Editing Archimedean property (section)

== History and origin of the name of the Archimedean property ==

The concept was named by [[Otto Stolz]] (in the 1880s) after the [[ancient Greece|ancient Greek]] geometer and physicist [[Archimedes]] of [[Syracuse, Italy|Syracuse]].

The Archimedean property appears in Book V of [[Euclid's Elements|Euclid's ''Elements'']] as Definition 4:

{{Blockquote|Magnitudes are said to have a ratio to one another which can, when multiplied, exceed one another.}}

Because Archimedes credited it to [[Eudoxus of Cnidus]] it is also known as the "Theorem of Eudoxus" or the ''Eudoxus axiom''.<ref name="Knopp1951">{{cite book|last=Knopp|first=Konrad|author-link=Konrad Knopp|title=Theory and Application of Infinite Series|url=https://archive.org/details/theoryapplicatio00knop|url-access=registration|edition=English 2nd|page=[https://archive.org/details/theoryapplicatio00knop/page/7 7]|year=1951|publisher=Blackie & Son, Ltd.|location=London and Glasgow|isbn=0-486-66165-2}}</ref>

[[Archimedes's use of infinitesimals|Archimedes used infinitesimals]] in [[heuristic]] arguments, although he denied that those were finished [[mathematical proof]]s.